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Simplifying 31 = -3(1 + r) + 5(r + 4) 31 = (1 * -3 + r * -3) + 5(r + 4) 31 = (-3 + -3r) + 5(r + 4) Reorder the terms: 31 = -3 + -3r + 5(4 + r) 31 = -3 + -3r + (4 * 5 + r * 5) 31 = -3 + -3r + (20 + 5r) Reorder the terms: 31 = -3 + 20 + -3r + 5r Combine like terms: -3 + 20 = 17 31 = 17 + -3r + 5r Combine like terms: -3r + 5r = 2r 31 = 17 + 2r Solving 31 = 17 + 2r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2r' to each side of the equation. 31 + -2r = 17 + 2r + -2r Combine like terms: 2r + -2r = 0 31 + -2r = 17 + 0 31 + -2r = 17 Add '-31' to each side of the equation. 31 + -31 + -2r = 17 + -31 Combine like terms: 31 + -31 = 0 0 + -2r = 17 + -31 -2r = 17 + -31 Combine like terms: 17 + -31 = -14 -2r = -14 Divide each side by '-2'. r = 7 Simplifying r = 7
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